How large is it?

PM may be strong enough, if there isn't too much stress applied to the moving parts.

You may be able to fill larger voids with thin plastic storage bags (twist-tie type), filled with the small 'beads' used to fill bean bag chairs. Secure in place, and then form papier mache over them.

Or, if you know the shape you need and can decently replicate it in clay or with other (temporary) forms, cover the form with thin plastic film and cover with several layers of PM and let dry thoroughly, then trim to fit, and attach.

Just some thoughts....

Sue

Again, how large is it? Six inches? Eighteen inches? Six feet?

Are you trying to duplicate the original rat?

Chicken wire is hard to work with, and harder to cover smoothly. What about buying some pink or blue insulation foam and carving it to at least the approximate shape(s)? You could do sections, ears, cheeks, nose, etc, and then cement them together to form the full shape. Then you could cover the whole piece with plastic wrap (taping where needed), and then start applying papier mache strips. The more layers you use, the stronger it will be.

Do you have a design to copy?

Sue

I think that paper laminate would be adequate for what you want but you would have to build it up to be strong enough.
First you need a mould (mold in US).  Clay is good for this, with a fine plastic covering.   Lay paper alternate newspaper and kraft to about twelve thicknesses, allowing it to dry in between each three layers.
There will be a bit of distortion but I don't think it should be too much.  Keep your paste as thick as you can manage and use it sparingly.  The wetter everything is the more it will distort.
I would put a very thin layer of fine pulp over it for real strength but this is getting a bit sophisticated if you are a beginner.
DavidO